35 children have been abandoned in the state. It's a cry for help.

LINCOLN, NEB. — First Melyssa Cowburn's 5-year-old child tried to bash in a baby's head with a hammer. Then he set the shower curtain on fire. The next day he plugged all the sinks and toilets in their apartment and flooded the place.

Cowburn and her husband had tried unsuccessfully to get their insurance company to pay for mental health treatment for the boy. The difficulty she had keeping him under control had already helped drive her to attempt suicide last year. Now she felt she had only one option: She flew with her child to Nebraska last week and tearfully left him there.

This state has become notorious for being the one place in the country with a law whose wording allows parents to abandon children up to age 18. Its unique safe-haven law -- which was intended to let parents leave unwanted infants at hospitals without legal consequences -- took effect in September, and since then 35 children have been abandoned, almost all of them 11 or older.

The Nebraska Legislature has spent this week in a special session, frantically trying to revise the law. It is expected to be amended today to allow abandonment only of infants up to 30 days old.

But children's advocates as well as parents like Cowburn say the state has done nothing to address the problem exposed by the safe-haven law: desperate families quietly struggling to raise mentally ill children with little help from the government. "There are parents like me who really need help," Cowburn said. "I don't know how to help him. I don't know what else to do."

Nebraska's unicameral Legislature has vowed to address the problem when it meets for its regular session in January. On Thursday, it created a special committee to formulate proposals during the next two months.

"It has been a blessing in disguise," state Sen. Amanda McGill, who chairs the committee, said of the response to the safe-haven law. "It has brought to light a serious problem."

"These parents were at wit's end," McGill said. "People don't want to give up their kids. They just want to get them help."

The administration of Republican Gov. Dave Heineman, which faces a potential budget deficit next year, has been cool to the suggestion that the flood of abandoned children shows a need to patch holes in the state's safety net. Todd Landry, head of the state's child welfare agency, said 75% of the Nebraska children were receiving some type of assistance from the government.

"We really want to emphasize to our families: Don't quit," Landry said. "I know that's really hard for families. These are frustrating situations. . . . It can take many tries before a treatment works."

Every state has a safe-haven law, intended to allow mothers who might otherwise abandon unwanted babies in unsafe places to legally leave them at hospitals. Nebraska became the last state to adopt such a policy when it passed its bill in February. Unlike in other states, however, lawmakers did not set an age limit for abandoned children.

The bill's supporters say they could not have anticipated what happened when it went into effect. On Sept. 13, two boys, 11 and 15, were dropped off by two families at hospitals in Omaha and Lincoln. The parents said each child had behavioral problems; one family feared the boy was in a violent gang but said child-welfare workers told the family they could not take him unless he committed a crime.

Soon the numbers snowballed. Gary Staton, a father of 10, left nine of his children at an Omaha hospital after his wife died. A few children arrived from other states. Teri Martin drove her 13-year-old adopted son from Michigan to leave him in Omaha in hopes of scaring him straight. Child-welfare officials in Michigan said the boy appeared to have been abused, and they removed Martin's three other children from her home.

The abandoned children were generally placed in foster homes or with relatives, though a few have required full-time residential treatment.

Some parents say it has been the only way to ensure that their child gets help.

Lavennia Coover's insurance covered only short hospital stays for her 11-year-old son, who has bipolar disorder. Despairing of getting help from the state in her rural northern Nebraska town, she trekked to Omaha last month and left her son at a hospital there.

"I am tired of being labeled a bad parent by people in power who have no idea what my life is like in my home," Coover told the Legislature's Judiciary Committee this week.

Children's advocates have long complained that Nebraska does not give adequate support to troubled youth. Its spending on child care and mental health is among the lowest in the nation, and its rate of foster care placement among the highest.

"This is not just something that's come up lately," said state Sen. Gwen Howard, a former state Health and Human Services case manager. "This is like a tsunami that's been building."